(a) Explanation Given information: The radius ( r ) of disk is 250 mm. The length ( l ) of the rod AB is 650 mm. The rod is displaced ( θ m ) for the position of 2 ° . Assume the acceleration due to gravity ( g ) is 9.8 m/s 2 . Calculation: Show the free body diagram equation as in Figure (1). Write the expression for the mass moment of inertia ( I ¯ ) : I ¯ = 1 2 m r 2 The angle ( α ) is equal to the angular acceleration θ ¨ . Write the expression for the tangential acceleration ( a t ) : a t = l α Substitute θ ¨ for α . a t = l θ ¨ The external forces in the system are tension in the force due to the mass of the disk. The effective couple in the system is I ¯ α . Take moment about B in the system for external forces. ( ∑ M B ) e x t e r n a l = − m g l sin θ For small oscillation sin θ ≈ θ , ( ∑ M B ) e x t e r n a l = − m g l θ Take moment about B in the system for effective forces. ( ∑ M B ) e f f e c t i v e = I ¯ α + m a t l The disk is free to rotate and is in curvilinear translation so, I ¯ α is equal to zero. Substitute 0 for I ¯ α and l θ ¨ for a t . ( ∑ M B ) e f f e c t i v e = 0 + m ( l θ ¨ ) l = m l 2 θ ¨ Equate the moment about B in the system for external and effective forces (b) To determine The magnitude of the maximum velocity ( v m ) B of point B assuming that the disk is riverted to the rod at A .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

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Chapter 19.2, Problem 19.60P

(a)

To determine

The magnitude of the maximum velocity (vm)A of point A assuming that the disk is free to rotate in a bearing at A.

(b)

To determine

The magnitude of the maximum velocity (vm)B of point B assuming that the disk is riverted to the rod at A.

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Chapter 19.2, Problem 19.59P

Chapter 19.2, Problem 19.61P

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Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The magnitude of the maximum velocity ( v m ) A of point A assuming that the disk is free to rotate in a bearing at A .

Solution Summary: The author shows the free body diagram equation as in Figure (1). Write the expression for the mass moment of inertia and the tangential acceleration.

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The magnitude of the maximum velocity (vm)A of point A assuming that the disk is free to rotate in a bearing at A.

The magnitude of the maximum velocity (vm)B of point B assuming that the disk is riverted to the rod at A.

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Chapter 19 Solutions